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A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service islan The joint pmf of X and Y appears in the accompanying tabulation. p(x,y) X 0 1 0 0.10 0.03 0.02 1 0.06 0.20 0.08 2 0.05 0.14 0.32 (a) What is P(X= 1 and Y= 1)? P(X = 1 and Y = 1) | 2 (b) Compute P(X ≤ 1 and Y ≤ I). P(X ≤ 1 and Y≤1)=[ (c) Give a word description of the event (X 0 and Y # 0). O One hose is in use on one island. O At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on both islands. Compute the probability of this event. P(X0 and Y 0)-[

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service islan The joint pmf of X and Y appears in the accompanying tabulation. p(x,y) X 0 1 0 0.10 0.03 0.02 1 0.06 0.20 0.08 2 0.05 0.14 0.32 (a) What is P(X= 1 and Y= 1)? P(X = 1 and Y = 1) | 2 (b) Compute P(X ≤ 1 and Y ≤ I). P(X ≤ 1 and Y≤1)=[ (c) Give a word description of the event (X 0 and Y # 0). O One hose is in use on one island. O At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on both islands. Compute the probability of this event. P(X0 and Y 0)-[

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x, y) (a) What is P(X= 1 and Y= 1)? P(X = 1 and Y = 1) = 0 (b) Compute P(X ≤ 1 and Y≤1). P(X ≤ 1 and Y ≤ 1) = | 0 0.10 0.03 0.02 0.06 0.20 0.08 2 0.05 0.14 0.32 1 (c) Give a word description of the event (X0 and Y 0} X O One hose is in use on one island. O At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on both islands. Compute the probability of this event. P(X 0 and Y# 0) = Py(y) (d) Compute the marginal pmf of X. 0 P(X ≤ 1) = Py(x) Compute the marginal pmf of Y. 1 1 Using p(x), what is P(X ≤ 1)? (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(x, y) = Px(x). Py(y). OX and Y are independent because P(x, y) ‡ Px(x) · Py(y).
Transcribed Image Text:A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x, y) (a) What is P(X= 1 and Y= 1)? P(X = 1 and Y = 1) = 0 (b) Compute P(X ≤ 1 and Y≤1). P(X ≤ 1 and Y ≤ 1) = | 0 0.10 0.03 0.02 0.06 0.20 0.08 2 0.05 0.14 0.32 1 (c) Give a word description of the event (X0 and Y 0} X O One hose is in use on one island. O At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on both islands. Compute the probability of this event. P(X 0 and Y# 0) = Py(y) (d) Compute the marginal pmf of X. 0 P(X ≤ 1) = Py(x) Compute the marginal pmf of Y. 1 1 Using p(x), what is P(X ≤ 1)? (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(x, y) = Px(x). Py(y). OX and Y are independent because P(x, y) ‡ Px(x) · Py(y).
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